Afghan President Hamid Karzai has accepted an invitation from U.S. President Barack Obama for critical talks on Afghanistan's future.

At a joint press conference with U.S. Defense Secretary Leon Panetta in Kabul on December 13, Karzai said he will discuss the number of U.S. troops that will stay in Afghanistan after international forces end their combat mission there in 2014.

"Tonight, I am pleased to inform you that the United States, through our ambassador, has issued a formal invitation to President Karzai from President Obama to meet in Washington during the week of January 7 to discuss a shared vision of Afghanistan beyond 2014," Panetta said.

Panetta said he and Karzai had discussed the terms of the future security arrangements between the two countries after 2014.

"Our two governments are working together on a bilateral security agreement that will establish the terms for our long-term security presence – to include a joint agreement on that enduring presence that I discussed," Panetta said.

Reports say one of the sticking points is whether U.S. troops will be granted immunity if they break Afghan law.

Officials say the White House is considering plans that call for between 6,000 and 10,000 U.S. troops to stay in Afghanistan to help maintain stability and to prevent Al-Qaeda and other terrorist groups from becoming a strong force again.

Panetta also praised the growing role the Afghan police and army are playing in maintaining security.

However, a suicide bomber struck outside a U.S. base in southern Afghanistan hours after a visit by Panetta, highlighting the security challenges Afghanistan faces.

Reports said one U.S. soldier was killed and three other U.S. troops wounded in the attack at the air base in Kandahar.

Panetta dismissed the attack as a desperate and futile attempt by insurgents to sow chaos in Afghanistan.

At Kandahar airfield, the top NATO commander of the southern region of Afghanistan, Major General Robert Abrams, said he would need fewer troops there next year because of security gains and the growing capability of the Afghans.